Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases calculated from the sum of the user group releases. The proportion of total rockfish harvested by user group, \(pH_{ayu}\), was assumed to be the mean of \(pH_{(pelagic)ayu}\), \(pH_{(yelloweye)ayu}\) and \(pH_{(nonpel-nonYE)ayu}\) weighted by the relative harvest \(H_{(comp)ayu}\) such that

\[\begin{equation} R_{ayu}~=~ \frac{\sum ({H_{(comp)ayu} * pH_{(comp)ayu})}}{\sum {H_{(comp)ayu}}} \end{equation}\]

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

**Figure 13.**- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of all rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pH 34 2.806582
mu_beta0_pH 5 2.717565
beta1_pH 38 2.685641
beta3_pH 35 2.646947
beta2_yellow 5 2.547205
beta3_yellow 6 2.075576
beta3_pelagic 7 1.984376
beta0_pelagic 7 1.968196
beta4_pelagic 1 1.703798
beta1_pelagic 9 1.585216
beta2_pelagic 7 1.573707
tau_beta0_pelagic 2 1.475721
beta0_yellow 7 1.470428
parameter n badRhat_avg
beta1_yellow 6 1.458033
beta2_pH 43 1.371892
sd_comp 1 1.253596
tau_beta0_pH 6 1.248759
tau_beta0_yellow 2 1.240215
beta2_black 2 1.228344
beta1_black 1 1.171283
beta0_black 2 1.156913
beta4_yellow 1 1.138539
beta_H 1 1.129140
beta3_black 1 1.122805
mu_beta0_yellow 1 1.113740
mu_beta0_pelagic 1 1.113686
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
beta0_black 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0
beta0_pelagic 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0
beta0_pH 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1
beta0_yellow 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1
beta1_black 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
beta1_pelagic 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1
beta1_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta1_yellow 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0
beta2_black 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0
beta2_pelagic 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0
beta2_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta2_yellow 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0
beta3_black 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
beta3_pelagic 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0
beta3_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta3_yellow 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0
beta4_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
beta4_yellow 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
mu_beta0_pelagic 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
mu_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.117 0.082 -0.269 -0.121 0.055
mu_bc_H[2] -0.095 0.044 -0.171 -0.098 0.002
mu_bc_H[3] -0.442 0.069 -0.565 -0.446 -0.301
mu_bc_H[4] -0.981 0.195 -1.367 -0.975 -0.607
mu_bc_H[5] 0.802 0.869 -0.237 0.629 2.915
mu_bc_H[6] -2.231 0.307 -2.819 -2.233 -1.624
mu_bc_H[7] -0.443 0.106 -0.655 -0.441 -0.239
mu_bc_H[8] 0.259 0.360 -0.342 0.223 1.049
mu_bc_H[9] -0.293 0.127 -0.549 -0.290 -0.046
mu_bc_H[10] -0.113 0.073 -0.247 -0.116 0.039
mu_bc_H[11] -0.107 0.039 -0.180 -0.108 -0.029
mu_bc_H[12] -0.246 0.112 -0.490 -0.241 -0.041
mu_bc_H[13] -0.139 0.078 -0.298 -0.138 0.013
mu_bc_H[14] -0.292 0.093 -0.479 -0.289 -0.115
mu_bc_H[15] -0.326 0.050 -0.419 -0.328 -0.224
mu_bc_H[16] -0.196 0.389 -0.895 -0.215 0.650
mu_bc_R[1] 1.458 0.182 1.107 1.456 1.817
mu_bc_R[2] 1.500 0.077 1.344 1.502 1.646
mu_bc_R[3] 1.417 0.148 1.121 1.419 1.693
mu_bc_R[4] 0.972 0.221 0.499 0.985 1.365
mu_bc_R[5] 1.246 0.452 0.337 1.248 2.108
mu_bc_R[6] -1.586 0.447 -2.434 -1.576 -0.713
mu_bc_R[7] 0.479 0.206 0.048 0.489 0.867
mu_bc_R[8] 0.544 0.198 0.147 0.550 0.916
mu_bc_R[9] 0.464 0.186 0.058 0.476 0.793
mu_bc_R[10] 1.374 0.170 1.031 1.375 1.716
mu_bc_R[11] 1.210 0.057 1.093 1.211 1.321
mu_bc_R[12] 1.023 0.150 0.722 1.027 1.311
mu_bc_R[13] 1.058 0.094 0.881 1.056 1.246
mu_bc_R[14] 1.029 0.140 0.732 1.037 1.294
mu_bc_R[15] 0.809 0.086 0.636 0.810 0.978
mu_bc_R[16] 1.185 0.110 0.953 1.189 1.390
tau_pH[1] 3.093 0.334 2.484 3.074 3.766
tau_pH[2] 1.225 0.802 0.445 0.820 2.731
tau_pH[3] 2.864 0.442 2.090 2.831 3.805
tau_pH[4] 5.982 2.497 2.790 5.479 12.360
tau_pH[5] 1.217 1.744 0.113 0.319 5.809
beta0_pH[1,1] 0.642 0.200 0.251 0.637 1.072
beta0_pH[2,1] 1.313 0.173 0.948 1.308 1.639
beta0_pH[3,1] 1.292 0.249 0.827 1.279 1.810
beta0_pH[4,1] 1.557 0.248 1.056 1.556 2.062
beta0_pH[5,1] -1.094 0.439 -1.905 -1.106 -0.173
beta0_pH[6,1] -0.843 0.514 -2.125 -0.748 -0.078
beta0_pH[7,1] -0.216 0.423 -1.074 -0.218 0.585
beta0_pH[8,1] -0.692 0.280 -1.246 -0.685 -0.149
beta0_pH[9,1] -0.841 0.391 -1.554 -0.833 -0.138
beta0_pH[10,1] 0.407 0.189 0.034 0.406 0.792
beta0_pH[11,1] -0.095 0.353 -0.658 -0.168 0.613
beta0_pH[12,1] 0.549 0.263 0.040 0.562 1.135
beta0_pH[13,1] -0.743 0.256 -1.280 -0.709 -0.312
beta0_pH[14,1] -0.450 0.617 -1.569 -0.375 0.609
beta0_pH[15,1] -0.646 0.387 -1.307 -0.676 0.406
beta0_pH[16,1] -1.036 0.960 -3.050 -1.110 0.716
beta0_pH[1,2] 2.792 0.274 2.213 2.805 3.292
beta0_pH[2,2] 2.841 0.288 2.208 2.872 3.298
beta0_pH[3,2] 2.831 0.341 2.076 2.860 3.437
beta0_pH[4,2] 2.798 0.215 2.378 2.792 3.231
beta0_pH[5,2] 4.122 1.412 1.928 3.957 7.142
beta0_pH[6,2] 3.143 0.335 2.498 3.140 3.800
beta0_pH[7,2] 2.022 0.313 1.400 2.008 2.670
beta0_pH[8,2] 2.881 0.271 2.353 2.876 3.420
beta0_pH[9,2] 3.525 0.390 2.708 3.517 4.269
beta0_pH[10,2] 3.789 0.333 3.143 3.787 4.438
beta0_pH[11,2] -2.772 2.617 -5.413 -4.460 1.796
beta0_pH[12,2] -4.576 0.709 -5.815 -4.651 -2.776
beta0_pH[13,2] -4.272 0.706 -5.602 -4.358 -2.679
beta0_pH[14,2] -4.791 0.812 -6.026 -4.925 -2.763
beta0_pH[15,2] -4.165 0.669 -5.034 -4.290 -2.854
beta0_pH[16,2] -4.311 0.946 -5.682 -4.507 -1.532
beta0_pH[1,3] 1.275 0.594 -1.285 1.373 1.800
beta0_pH[2,3] 1.838 0.324 1.172 1.869 2.359
beta0_pH[3,3] 1.936 0.290 1.399 1.921 2.552
beta0_pH[4,3] 2.241 0.566 1.165 2.313 3.066
beta0_pH[5,3] 0.687 0.895 -0.658 0.536 3.046
beta0_pH[6,3] -0.007 0.789 -1.965 0.167 1.110
beta0_pH[7,3] 0.370 0.541 -1.102 0.527 1.025
beta0_pH[8,3] 0.327 0.174 -0.013 0.332 0.658
beta0_pH[9,3] 0.160 0.306 -0.503 0.176 0.692
beta0_pH[10,3] 0.644 0.321 -0.069 0.663 1.200
beta0_pH[11,4] -0.828 2.319 -4.277 -1.143 2.603
beta0_pH[12,4] -1.029 2.381 -3.743 -2.357 2.846
beta0_pH[13,4] -1.129 2.148 -3.457 -2.312 2.260
beta0_pH[14,4] -1.185 2.445 -4.395 -2.009 2.579
beta0_pH[15,4] -1.962 2.609 -5.140 -3.486 1.952
beta0_pH[16,4] -1.766 2.687 -4.748 -3.273 2.259
beta0_pH[11,5] 1.274 1.363 -1.142 1.666 3.700
beta0_pH[12,5] 0.353 2.752 -3.139 0.653 7.363
beta0_pH[13,5] 1.292 1.319 -0.651 1.379 4.071
beta0_pH[14,5] -0.113 1.390 -2.549 -0.468 2.427
beta0_pH[15,5] 1.075 1.427 -1.567 1.565 3.390
beta0_pH[16,5] -0.923 3.133 -8.911 -0.460 2.603
beta1_pH[1,1] 2.777 0.351 2.143 2.757 3.525
beta1_pH[2,1] 2.444 0.305 1.896 2.419 3.112
beta1_pH[3,1] 2.459 0.413 1.701 2.439 3.404
beta1_pH[4,1] 2.819 0.455 2.064 2.765 3.764
beta1_pH[5,1] 2.518 0.454 1.665 2.517 3.378
beta1_pH[6,1] 3.528 1.106 2.009 3.301 6.266
beta1_pH[7,1] 1.572 0.716 0.551 1.436 3.253
beta1_pH[8,1] 3.335 0.650 2.164 3.268 4.688
beta1_pH[9,1] 2.498 0.470 1.699 2.505 3.532
beta1_pH[10,1] 2.044 0.296 1.447 2.038 2.654
beta1_pH[11,1] 3.619 0.404 2.792 3.685 4.254
beta1_pH[12,1] 2.591 0.307 1.968 2.580 3.175
beta1_pH[13,1] 3.632 0.346 3.049 3.600 4.372
beta1_pH[14,1] 3.759 0.625 2.693 3.698 4.910
beta1_pH[15,1] 4.039 0.576 2.676 4.099 5.012
beta1_pH[16,1] 4.266 1.063 2.408 4.297 6.641
beta1_pH[1,2] 0.668 1.567 0.000 0.157 4.560
beta1_pH[2,2] 0.917 3.841 0.000 0.132 6.053
beta1_pH[3,2] 0.639 2.106 0.000 0.214 1.832
beta1_pH[4,2] 1.274 4.585 0.000 0.133 11.255
beta1_pH[5,2] 120.901 261.961 0.000 0.002 997.883
beta1_pH[6,2] 0.197 1.116 0.000 0.001 1.688
beta1_pH[7,2] 0.131 0.951 0.000 0.000 0.771
beta1_pH[8,2] 0.190 2.118 0.000 0.000 0.747
beta1_pH[9,2] 0.263 1.730 0.000 0.000 1.662
beta1_pH[10,2] 0.228 4.816 0.000 0.001 1.144
beta1_pH[11,2] 6.598 3.595 3.132 6.634 10.740
beta1_pH[12,2] 6.533 0.769 4.795 6.549 8.109
beta1_pH[13,2] 6.803 0.775 5.050 6.890 8.298
beta1_pH[14,2] 6.203 1.393 3.310 6.725 8.028
beta1_pH[15,2] 6.731 0.727 5.283 6.870 7.715
beta1_pH[16,2] 6.520 1.452 2.628 7.100 8.086
beta1_pH[1,3] 2.032 0.943 1.198 1.879 5.113
beta1_pH[2,3] 0.663 0.448 0.002 0.638 1.604
beta1_pH[3,3] 0.841 0.364 0.014 0.880 1.473
beta1_pH[4,3] 0.852 0.614 0.003 0.824 2.066
beta1_pH[5,3] 4.981 5.437 1.222 3.342 20.010
beta1_pH[6,3] 3.325 3.551 0.332 2.392 14.116
beta1_pH[7,3] 1.548 1.672 0.134 1.046 5.344
beta1_pH[8,3] 2.697 0.339 2.030 2.699 3.340
beta1_pH[9,3] 1.903 0.371 1.210 1.899 2.659
beta1_pH[10,3] 2.729 0.410 2.018 2.693 3.639
beta1_pH[11,4] 3.904 2.663 0.008 4.728 7.466
beta1_pH[12,4] 4.037 2.500 0.008 5.376 7.023
beta1_pH[13,4] 3.570 2.286 0.008 4.761 6.177
beta1_pH[14,4] 3.804 2.575 0.007 4.584 7.163
beta1_pH[15,4] 4.102 2.729 0.005 5.701 7.207
beta1_pH[16,4] 4.011 2.685 0.008 5.618 6.924
beta1_pH[11,5] 4.612 8.188 0.001 2.008 22.307
beta1_pH[12,5] 9.525 22.554 0.001 3.606 81.294
beta1_pH[13,5] 2.845 3.242 0.000 1.115 10.142
beta1_pH[14,5] 3.007 3.650 0.000 2.159 13.763
beta1_pH[15,5] 11.400 11.280 0.001 7.939 35.390
beta1_pH[16,5] 4.373 5.127 0.000 2.853 17.083
beta2_pH[1,1] 0.524 0.178 0.300 0.483 0.969
beta2_pH[2,1] 0.485 0.237 0.201 0.428 1.103
beta2_pH[3,1] 0.504 0.282 0.190 0.436 1.224
beta2_pH[4,1] 0.413 0.188 0.176 0.372 0.894
beta2_pH[5,1] 1.187 0.752 0.254 1.053 3.056
beta2_pH[6,1] 0.259 0.195 0.095 0.215 0.695
beta2_pH[7,1] 0.440 0.653 0.002 0.151 2.255
beta2_pH[8,1] 0.387 0.269 0.170 0.317 1.154
beta2_pH[9,1] 0.529 0.293 0.157 0.470 1.302
beta2_pH[10,1] 0.673 0.314 0.259 0.612 1.438
beta2_pH[11,1] 0.838 0.234 0.505 0.798 1.429
beta2_pH[12,1] 1.342 0.426 0.753 1.275 2.332
beta2_pH[13,1] 0.790 0.314 0.362 0.743 1.503
beta2_pH[14,1] 0.966 0.280 0.566 0.921 1.634
beta2_pH[15,1] 0.698 0.241 0.377 0.656 1.308
beta2_pH[16,1] 0.626 0.265 0.257 0.577 1.258
beta2_pH[1,2] -0.279 41.057 -37.441 0.636 39.767
beta2_pH[2,2] -2.746 37.905 -54.304 -1.091 37.567
beta2_pH[3,2] -0.579 34.906 -46.974 -1.843 55.897
beta2_pH[4,2] -2.682 21.642 -50.334 -1.902 29.825
beta2_pH[5,2] -1.340 100.455 -229.659 -0.604 172.456
beta2_pH[6,2] -14.357 101.111 -340.163 -1.418 192.014
beta2_pH[7,2] 12.393 83.212 -139.840 -0.069 271.041
beta2_pH[8,2] 0.858 75.508 -102.606 -1.407 162.546
beta2_pH[9,2] 37.641 151.468 -81.202 -0.681 600.808
beta2_pH[10,2] -3.354 56.208 -178.211 -0.699 127.071
beta2_pH[11,2] -7.150 8.484 -28.204 -4.864 -0.477
beta2_pH[12,2] -3.726 4.375 -13.322 -2.867 -0.662
beta2_pH[13,2] -4.917 6.305 -20.446 -2.957 -1.342
beta2_pH[14,2] -0.331 8.881 -9.792 -2.710 17.725
beta2_pH[15,2] -7.445 7.702 -28.489 -5.152 -1.378
beta2_pH[16,2] -3.608 9.668 -22.804 -4.118 12.649
beta2_pH[1,3] 18.581 59.613 0.211 3.857 160.971
beta2_pH[2,3] 18.016 66.326 -21.683 3.074 198.415
beta2_pH[3,3] -14.765 94.236 -142.511 -3.352 17.027
beta2_pH[4,3] 3.050 103.229 -105.137 0.212 94.816
beta2_pH[5,3] 4.662 9.429 -2.834 4.020 15.638
beta2_pH[6,3] 5.503 10.372 0.314 4.161 18.720
beta2_pH[7,3] 3.937 7.444 -1.814 3.615 11.578
beta2_pH[8,3] 7.194 9.740 1.761 5.217 27.781
beta2_pH[9,3] 5.973 8.133 1.357 4.396 21.050
beta2_pH[10,3] 5.147 13.456 0.529 3.771 13.365
beta2_pH[11,4] 0.051 1.938 -2.078 -0.227 4.281
beta2_pH[12,4] -0.001 2.090 -1.606 -0.682 5.907
beta2_pH[13,4] -0.625 2.568 -4.716 -0.995 5.328
beta2_pH[14,4] 0.893 2.729 -2.780 0.539 7.308
beta2_pH[15,4] -1.379 2.760 -6.372 -1.417 4.014
beta2_pH[16,4] -1.888 2.811 -8.785 -1.293 1.095
beta2_pH[11,5] -1.701 6.127 -11.677 -1.881 6.973
beta2_pH[12,5] -1.332 6.315 -11.282 -1.298 10.287
beta2_pH[13,5] -1.015 6.025 -10.576 -1.198 8.369
beta2_pH[14,5] -0.939 4.355 -9.386 -0.508 6.469
beta2_pH[15,5] -0.493 5.746 -9.537 0.597 8.075
beta2_pH[16,5] -0.671 6.406 -9.784 -0.684 10.381
beta3_pH[1,1] 35.451 0.922 33.737 35.429 37.392
beta3_pH[2,1] 34.387 1.291 32.049 34.430 37.007
beta3_pH[3,1] 34.895 1.012 32.997 34.884 36.801
beta3_pH[4,1] 35.024 1.160 32.807 35.007 37.531
beta3_pH[5,1] 28.080 1.993 26.328 27.458 34.445
beta3_pH[6,1] 36.571 3.174 31.302 36.323 44.221
beta3_pH[7,1] 31.254 7.015 19.998 30.562 45.179
beta3_pH[8,1] 38.444 1.613 35.341 38.565 41.936
beta3_pH[9,1] 30.786 2.071 27.336 30.606 35.717
beta3_pH[10,1] 33.273 1.135 31.212 33.176 36.126
beta3_pH[11,1] 31.087 0.465 30.215 31.081 32.038
beta3_pH[12,1] 30.594 0.464 29.640 30.603 31.512
beta3_pH[13,1] 32.515 0.596 31.292 32.541 33.588
beta3_pH[14,1] 32.241 0.671 31.107 32.211 33.738
beta3_pH[15,1] 32.395 0.693 31.215 32.361 33.842
beta3_pH[16,1] 31.429 1.004 29.509 31.397 33.839
beta3_pH[1,2] 31.802 12.056 12.179 32.468 47.985
beta3_pH[2,2] 29.836 16.926 5.144 30.603 51.699
beta3_pH[3,2] 34.940 13.177 17.350 37.297 46.323
beta3_pH[4,2] 29.764 7.860 16.979 30.607 44.494
beta3_pH[5,2] 39.268 59.683 -69.518 32.816 198.809
beta3_pH[6,2] 33.469 56.646 -85.479 30.984 168.146
beta3_pH[7,2] 28.647 39.177 -63.483 29.974 124.027
beta3_pH[8,2] 23.120 53.108 -140.122 29.776 119.114
beta3_pH[9,2] 7.667 59.652 -153.672 27.345 83.273
beta3_pH[10,2] 33.255 45.897 -75.466 31.972 141.119
beta3_pH[11,2] 34.445 13.318 4.904 43.212 43.734
beta3_pH[12,2] 42.960 0.564 41.388 43.094 43.757
beta3_pH[13,2] 43.661 0.279 43.072 43.685 44.133
beta3_pH[14,2] 36.913 9.845 10.922 43.040 43.724
beta3_pH[15,2] 43.382 0.254 42.792 43.396 43.823
beta3_pH[16,2] 37.562 8.488 20.782 43.322 43.759
beta3_pH[1,3] 39.913 1.341 35.712 40.073 41.610
beta3_pH[2,3] 38.233 7.841 24.747 37.489 54.763
beta3_pH[3,3] 39.500 4.495 30.036 41.236 43.230
beta3_pH[4,3] 37.008 12.358 8.200 39.731 58.074
beta3_pH[5,3] 32.355 9.380 11.167 33.897 49.392
beta3_pH[6,3] 35.335 7.973 25.293 33.602 56.112
beta3_pH[7,3] 37.890 13.097 15.241 35.668 63.446
beta3_pH[8,3] 41.488 0.247 41.019 41.491 41.937
beta3_pH[9,3] 33.890 0.499 33.027 33.862 34.909
beta3_pH[10,3] 35.872 0.651 34.098 36.005 36.820
beta3_pH[11,4] 38.782 6.029 29.187 42.227 46.247
beta3_pH[12,4] 38.440 5.935 27.117 42.151 43.318
beta3_pH[13,4] 39.772 5.924 29.239 43.021 48.693
beta3_pH[14,4] 33.649 6.843 23.637 30.507 43.359
beta3_pH[15,4] 40.353 7.814 27.098 43.331 53.106
beta3_pH[16,4] 39.982 6.619 28.657 43.439 49.763
beta3_pH[11,5] 45.859 61.288 -72.640 41.801 185.480
beta3_pH[12,5] 35.788 59.170 -103.563 40.211 153.652
beta3_pH[13,5] 40.896 65.061 -78.431 41.057 180.507
beta3_pH[14,5] 21.440 32.641 -70.627 39.857 45.696
beta3_pH[15,5] 73.043 43.143 39.498 44.009 166.030
beta3_pH[16,5] 29.645 18.979 -12.262 39.848 48.869
beta0_pelagic[1] 1.084 0.574 0.044 1.068 2.203
beta0_pelagic[2] 0.932 0.397 0.280 0.861 1.582
beta0_pelagic[3] 0.297 0.236 -0.248 0.338 0.688
beta0_pelagic[4] 0.300 0.234 -0.295 0.340 0.625
beta0_pelagic[5] 1.278 0.235 0.777 1.308 1.655
beta0_pelagic[6] 1.409 0.225 0.898 1.434 1.776
beta0_pelagic[7] 1.440 0.160 1.090 1.452 1.719
beta0_pelagic[8] 1.661 0.189 1.240 1.669 2.008
beta0_pelagic[9] 1.398 0.425 0.342 1.426 2.187
beta0_pelagic[10] 1.895 0.412 1.219 1.824 2.634
beta0_pelagic[11] 0.565 0.405 -0.316 0.627 1.072
beta0_pelagic[12] 1.645 0.155 1.342 1.648 1.940
beta0_pelagic[13] 0.157 0.639 -1.390 0.436 0.784
beta0_pelagic[14] 0.205 0.261 -0.373 0.250 0.643
beta0_pelagic[15] -0.262 0.171 -0.578 -0.290 0.111
beta0_pelagic[16] 0.344 0.161 0.014 0.357 0.641
beta1_pelagic[1] 1.266 0.674 0.061 1.262 2.502
beta1_pelagic[2] 0.832 0.535 0.022 0.938 1.797
beta1_pelagic[3] 0.795 0.282 0.333 0.753 1.382
beta1_pelagic[4] 0.947 0.272 0.530 0.915 1.590
beta1_pelagic[5] 0.530 0.662 0.016 0.405 1.578
beta1_pelagic[6] 0.516 0.651 0.018 0.392 1.871
beta1_pelagic[7] 0.489 0.682 0.014 0.325 2.733
beta1_pelagic[8] 0.895 0.584 0.088 0.788 2.396
beta1_pelagic[9] 1.584 0.536 0.700 1.519 2.938
beta1_pelagic[10] 0.878 0.577 0.040 0.853 2.257
beta1_pelagic[11] 1.874 1.202 0.012 2.002 4.118
beta1_pelagic[12] 2.245 0.323 1.661 2.238 2.891
beta1_pelagic[13] 2.303 1.126 0.359 2.003 5.248
beta1_pelagic[14] 2.835 0.624 1.890 2.737 4.293
beta1_pelagic[15] 2.096 0.533 0.371 2.224 2.635
beta1_pelagic[16] 3.001 0.407 2.329 2.964 3.900
beta2_pelagic[1] 1.675 1.809 -0.670 1.188 6.420
beta2_pelagic[2] 0.916 2.206 -4.262 0.297 6.054
beta2_pelagic[3] 1.859 1.765 0.138 1.261 6.640
beta2_pelagic[4] 2.301 1.764 0.154 1.892 6.749
beta2_pelagic[5] -1.543 2.866 -6.890 -1.615 5.177
beta2_pelagic[6] 1.427 2.758 -4.432 1.352 6.951
beta2_pelagic[7] -0.969 2.983 -6.700 -1.067 5.472
beta2_pelagic[8] -1.876 2.041 -6.607 -1.410 0.992
beta2_pelagic[9] 1.839 1.776 0.122 1.220 6.254
beta2_pelagic[10] 1.477 1.963 -2.883 1.334 5.398
beta2_pelagic[11] -0.393 2.097 -5.235 0.205 3.123
beta2_pelagic[12] 1.253 0.723 0.451 1.073 3.178
beta2_pelagic[13] 0.743 0.839 0.068 0.553 3.036
beta2_pelagic[14] 0.480 0.387 0.163 0.388 1.229
beta2_pelagic[15] 1.652 1.182 0.433 1.315 4.669
beta2_pelagic[16] 0.972 0.766 0.294 0.706 3.143
beta3_pelagic[1] 23.649 3.837 19.492 22.386 34.734
beta3_pelagic[2] 27.585 5.607 19.471 27.727 38.821
beta3_pelagic[3] 30.018 2.465 25.110 30.139 35.386
beta3_pelagic[4] 25.805 2.344 22.163 25.653 32.699
beta3_pelagic[5] 29.791 4.396 20.993 29.337 38.608
beta3_pelagic[6] 30.259 5.164 20.593 30.082 39.318
beta3_pelagic[7] 29.149 4.579 20.528 29.225 38.968
beta3_pelagic[8] 28.153 3.890 21.741 27.346 37.513
beta3_pelagic[9] 27.330 2.924 23.243 26.424 35.029
beta3_pelagic[10] 25.630 5.134 19.307 23.533 37.326
beta3_pelagic[11] 34.977 8.063 19.547 39.239 41.970
beta3_pelagic[12] 41.766 0.269 41.014 41.857 41.996
beta3_pelagic[13] 38.655 3.820 27.963 40.306 41.955
beta3_pelagic[14] 40.797 1.013 38.315 41.087 41.963
beta3_pelagic[15] 40.895 3.320 30.800 41.835 41.994
beta3_pelagic[16] 41.580 0.411 40.456 41.725 41.992
mu_beta0_pelagic[1] 0.628 0.537 -0.256 0.606 1.604
mu_beta0_pelagic[2] 1.509 0.263 1.064 1.499 2.018
mu_beta0_pelagic[3] 0.429 0.424 -0.490 0.456 1.199
tau_beta0_pelagic[1] 6.760 8.348 0.141 3.304 31.976
tau_beta0_pelagic[2] 22.813 33.581 0.875 9.317 132.060
tau_beta0_pelagic[3] 2.033 1.493 0.236 1.676 5.995
beta0_yellow[1] -0.583 0.190 -1.028 -0.568 -0.255
beta0_yellow[2] 0.281 0.419 -0.804 0.393 0.827
beta0_yellow[3] -0.337 0.161 -0.663 -0.329 -0.042
beta0_yellow[4] 0.041 0.766 -2.268 0.178 0.987
beta0_yellow[5] -1.118 0.480 -2.021 -1.136 -0.134
beta0_yellow[6] 0.149 0.218 -0.276 0.144 0.588
beta0_yellow[7] 0.311 0.876 -1.896 0.581 1.277
beta0_yellow[8] 0.610 0.609 -1.122 0.832 1.234
beta0_yellow[9] -0.099 0.283 -0.643 -0.086 0.385
beta0_yellow[10] 0.234 0.158 -0.085 0.234 0.540
beta0_yellow[11] -0.139 0.166 -0.480 -0.140 0.178
beta0_yellow[12] -3.630 0.500 -4.570 -3.652 -2.561
beta0_yellow[13] -3.425 0.760 -4.791 -3.361 -2.074
beta0_yellow[14] -1.246 1.042 -3.239 -0.825 -0.042
beta0_yellow[15] -2.300 0.556 -3.196 -2.401 -0.982
beta0_yellow[16] -0.506 0.244 -1.123 -0.468 -0.128
beta1_yellow[1] 0.595 0.685 0.017 0.407 2.384
beta1_yellow[2] 1.674 0.948 0.713 1.303 4.255
beta1_yellow[3] 0.744 0.227 0.354 0.729 1.267
beta1_yellow[4] 2.376 1.198 0.803 2.029 4.838
beta1_yellow[5] 3.261 1.199 1.327 3.128 6.223
beta1_yellow[6] 2.391 0.363 1.693 2.400 3.088
beta1_yellow[7] 1.523 1.338 0.070 1.147 5.099
beta1_yellow[8] 1.770 1.587 0.080 1.231 6.194
beta1_yellow[9] 1.496 0.394 0.790 1.490 2.225
beta1_yellow[10] 2.750 0.528 1.793 2.726 3.912
beta1_yellow[11] 1.467 0.971 0.233 1.220 3.744
beta1_yellow[12] 2.515 0.583 1.425 2.501 3.660
beta1_yellow[13] 3.691 1.093 1.983 3.489 6.061
beta1_yellow[14] 2.488 1.778 0.303 2.101 6.407
beta1_yellow[15] 1.771 0.520 0.811 1.795 2.737
beta1_yellow[16] 0.713 0.655 0.019 0.518 2.312
beta2_yellow[1] -1.614 2.618 -6.806 -1.527 4.355
beta2_yellow[2] -1.044 1.266 -4.681 -0.582 -0.052
beta2_yellow[3] -2.240 1.739 -6.573 -1.830 -0.163
beta2_yellow[4] 1.137 2.458 -2.470 -0.091 5.684
beta2_yellow[5] -3.004 1.877 -7.402 -2.653 -0.465
beta2_yellow[6] 3.227 1.794 0.923 2.761 8.241
beta2_yellow[7] 0.653 2.970 -5.666 0.758 6.220
beta2_yellow[8] -0.436 2.968 -5.861 -0.712 5.410
beta2_yellow[9] 3.426 1.781 0.401 3.218 7.381
beta2_yellow[10] -3.446 1.780 -7.541 -3.163 -0.773
beta2_yellow[11] -2.306 1.690 -6.223 -1.808 -0.317
beta2_yellow[12] -3.272 1.703 -7.301 -3.000 -0.579
beta2_yellow[13] -1.552 1.596 -5.463 -1.267 -0.087
beta2_yellow[14] -1.608 1.995 -6.872 -0.629 -0.036
beta2_yellow[15] -2.140 1.547 -5.408 -1.790 -0.133
beta2_yellow[16] -1.258 2.503 -6.154 -1.105 4.728
beta3_yellow[1] 28.537 4.824 19.938 28.736 37.649
beta3_yellow[2] 28.868 2.292 22.791 29.061 32.818
beta3_yellow[3] 32.642 2.060 28.426 32.689 36.468
beta3_yellow[4] 25.350 4.959 19.053 26.225 34.249
beta3_yellow[5] 32.948 1.378 29.911 33.095 35.025
beta3_yellow[6] 39.516 0.497 38.576 39.505 40.601
beta3_yellow[7] 28.026 3.784 21.102 27.816 36.704
beta3_yellow[8] 27.587 3.542 20.968 27.644 35.203
beta3_yellow[9] 37.362 1.009 35.606 37.430 38.651
beta3_yellow[10] 29.283 0.516 28.055 29.346 30.038
beta3_yellow[11] 31.603 2.014 29.131 31.162 36.477
beta3_yellow[12] 43.126 1.129 41.293 43.258 44.137
beta3_yellow[13] 39.957 5.529 29.609 44.083 44.968
beta3_yellow[14] 34.352 4.847 29.175 32.764 43.934
beta3_yellow[15] 42.225 4.727 29.556 44.305 44.970
beta3_yellow[16] 32.322 2.687 29.147 31.619 38.464
mu_beta0_yellow[1] -0.134 0.467 -1.143 -0.117 0.718
mu_beta0_yellow[2] 0.014 0.438 -0.923 0.029 0.866
mu_beta0_yellow[3] -1.573 0.847 -3.243 -1.573 0.208
tau_beta0_yellow[1] 6.621 11.988 0.235 3.020 43.692
tau_beta0_yellow[2] 4.577 10.671 0.232 1.593 42.098
tau_beta0_yellow[3] 0.369 0.306 0.038 0.278 1.179
beta0_black[1] -0.077 0.158 -0.397 -0.074 0.229
beta0_black[2] 1.732 0.224 1.187 1.761 2.091
beta0_black[3] 1.211 0.204 0.730 1.238 1.537
beta0_black[4] 1.848 0.353 0.807 1.918 2.298
beta0_black[5] 1.325 1.027 -1.180 1.345 3.361
beta0_black[6] 1.406 1.297 -0.870 1.347 3.618
beta0_black[7] 1.404 1.254 -0.715 1.357 3.636
beta0_black[8] 1.132 0.307 0.451 1.172 1.620
beta0_black[9] 1.695 0.491 0.767 1.691 2.573
beta0_black[10] 1.344 0.195 0.999 1.361 1.631
beta0_black[11] 3.287 0.327 2.215 3.345 3.694
beta0_black[12] 4.407 0.195 4.025 4.404 4.776
beta0_black[13] -0.062 0.225 -0.524 -0.055 0.372
beta0_black[14] 1.705 0.709 0.026 1.892 2.638
beta0_black[15] 0.995 0.378 0.053 1.066 1.543
beta0_black[16] 3.245 0.967 0.499 3.510 4.344
beta2_black[1] 3.141 1.688 0.790 2.848 7.274
beta2_black[2] -1.789 2.306 -6.224 -1.506 3.329
beta2_black[3] -0.270 3.201 -6.295 -0.467 6.130
beta2_black[4] -2.114 1.732 -6.132 -1.877 -0.063
beta2_black[5] 0.052 3.168 -5.908 0.032 6.408
beta2_black[6] -0.044 3.151 -6.352 -0.028 6.012
beta2_black[7] -0.006 3.134 -6.033 0.018 6.123
beta2_black[8] -2.994 2.276 -7.739 -2.771 1.236
beta2_black[9] -1.370 2.505 -6.413 -1.089 4.574
beta2_black[10] -1.228 2.369 -5.437 -1.261 4.637
beta2_black[11] -2.170 2.714 -6.977 -2.052 4.232
beta2_black[12] -3.080 1.676 -7.173 -2.773 -0.755
beta2_black[13] -2.315 1.635 -6.551 -1.834 -0.393
beta2_black[14] -0.908 1.365 -5.083 -0.325 -0.072
beta2_black[15] -1.717 1.984 -6.222 -1.232 1.158
beta2_black[16] 1.797 2.106 -2.310 1.440 6.496
beta3_black[1] 41.815 0.767 40.200 41.911 43.088
beta3_black[2] 29.825 7.836 19.229 30.512 44.287
beta3_black[3] 27.579 7.418 19.175 26.257 44.646
beta3_black[4] 32.844 3.486 22.430 32.797 38.773
beta3_black[5] 31.647 7.316 19.658 31.280 44.846
beta3_black[6] 32.171 7.334 19.745 32.165 44.908
beta3_black[7] 32.003 7.293 19.714 31.880 45.014
beta3_black[8] 29.096 7.991 20.316 23.445 43.257
beta3_black[9] 34.335 8.413 19.676 35.291 45.246
beta3_black[10] 26.769 8.191 19.251 23.005 45.097
beta3_black[11] 33.617 4.575 29.078 31.848 45.294
beta3_black[12] 32.865 0.595 31.527 32.934 33.815
beta3_black[13] 39.241 0.791 37.647 39.319 40.472
beta3_black[14] 38.355 3.836 30.225 38.490 45.402
beta3_black[15] 36.301 5.268 29.184 35.653 45.451
beta3_black[16] 33.479 4.088 29.117 32.089 43.523
beta4_black[1] -0.282 0.199 -0.661 -0.279 0.112
beta4_black[2] 0.282 0.184 -0.076 0.277 0.646
beta4_black[3] -0.999 0.188 -1.381 -0.998 -0.635
beta4_black[4] 0.655 0.227 0.225 0.651 1.089
beta4_black[5] -0.020 3.176 -6.254 -0.034 6.073
beta4_black[6] 0.068 3.108 -6.045 -0.027 6.314
beta4_black[7] -0.007 3.212 -6.505 0.116 6.135
beta4_black[8] -0.856 0.380 -1.624 -0.855 -0.114
beta4_black[9] 2.163 1.129 0.285 2.047 4.668
beta4_black[10] 0.028 0.187 -0.335 0.030 0.385
beta4_black[11] -0.686 0.230 -1.116 -0.688 -0.227
beta4_black[12] 0.579 0.344 -0.065 0.578 1.261
beta4_black[13] -1.295 0.226 -1.738 -1.294 -0.852
beta4_black[14] -0.043 0.247 -0.515 -0.049 0.435
beta4_black[15] -0.937 0.224 -1.374 -0.935 -0.506
beta4_black[16] -0.582 0.244 -1.040 -0.582 -0.094
mu_beta0_black[1] 1.031 0.903 -0.961 1.107 2.307
mu_beta0_black[2] 1.321 0.656 0.145 1.349 2.330
mu_beta0_black[3] 1.940 1.159 -0.849 2.087 3.712
tau_beta0_black[1] 1.267 1.184 0.045 0.952 4.385
tau_beta0_black[2] 15.038 22.036 0.117 5.745 80.267
tau_beta0_black[3] 0.330 0.238 0.028 0.282 0.904
beta0_dsr[11] -3.280 0.527 -4.746 -3.185 -2.485
beta0_dsr[12] 4.363 1.110 -0.085 4.583 5.181
beta0_dsr[13] -1.688 0.412 -2.517 -1.680 -0.871
beta0_dsr[14] -3.739 1.470 -4.925 -4.257 0.273
beta0_dsr[15] -2.089 0.721 -2.768 -2.272 0.180
beta0_dsr[16] -3.243 0.399 -4.019 -3.242 -2.467
beta1_dsr[11] 5.145 0.583 4.401 4.995 6.767
beta1_dsr[12] 4.415 1.876 1.318 4.192 8.791
beta1_dsr[13] 3.698 0.839 2.681 3.478 6.274
beta1_dsr[14] 6.276 1.816 1.300 6.914 7.676
beta1_dsr[15] 3.226 0.836 0.476 3.484 3.974
beta1_dsr[16] 6.018 0.415 5.205 6.021 6.843
beta2_dsr[11] -5.496 2.204 -9.027 -5.679 -0.522
beta2_dsr[12] -2.887 2.483 -7.230 -2.905 4.533
beta2_dsr[13] -1.510 1.386 -4.931 -1.022 -0.154
beta2_dsr[14] -2.794 3.050 -7.049 -3.366 5.828
beta2_dsr[15] -4.724 2.535 -8.784 -4.995 2.912
beta2_dsr[16] -5.691 1.553 -9.056 -5.578 -3.048
beta3_dsr[11] 43.535 0.232 43.240 43.494 44.238
beta3_dsr[12] 33.306 1.333 29.294 33.670 34.792
beta3_dsr[13] 42.056 1.925 37.014 42.968 43.701
beta3_dsr[14] 41.701 4.533 29.128 43.336 43.680
beta3_dsr[15] 42.597 3.055 29.544 43.401 43.781
beta3_dsr[16] 43.453 0.133 43.218 43.447 43.724
beta4_dsr[11] 0.769 0.237 0.315 0.766 1.238
beta4_dsr[12] 0.179 0.736 -1.170 0.132 1.788
beta4_dsr[13] -0.170 0.225 -0.606 -0.170 0.276
beta4_dsr[14] 0.256 0.351 -0.348 0.224 1.065
beta4_dsr[15] 1.069 0.215 0.640 1.069 1.484
beta4_dsr[16] 0.206 0.254 -0.293 0.204 0.685
beta0_slope[11] -2.047 0.166 -2.441 -2.031 -1.760
beta0_slope[12] -4.628 0.226 -4.978 -4.655 -4.146
beta0_slope[13] -1.829 0.421 -2.741 -1.745 -1.203
beta0_slope[14] -2.736 0.197 -3.129 -2.733 -2.355
beta0_slope[15] -1.986 0.552 -3.444 -1.785 -1.483
beta0_slope[16] -2.839 0.176 -3.167 -2.843 -2.479
beta1_slope[11] 4.423 0.314 3.844 4.414 5.072
beta1_slope[12] 4.957 0.617 3.752 4.948 6.179
beta1_slope[13] 3.097 0.778 2.042 2.914 5.050
beta1_slope[14] 5.805 0.685 4.616 5.770 7.237
beta1_slope[15] 2.171 0.585 1.266 2.066 3.755
beta1_slope[16] 5.319 0.411 4.519 5.322 6.144
beta2_slope[11] 6.015 1.515 3.375 5.875 9.147
beta2_slope[12] 3.111 1.655 1.001 2.693 7.037
beta2_slope[13] 1.348 1.425 0.194 0.633 5.130
beta2_slope[14] 1.602 0.897 0.775 1.346 4.341
beta2_slope[15] 2.857 2.251 0.109 2.788 7.564
beta2_slope[16] 5.288 1.631 2.529 5.124 8.953
beta3_slope[11] 43.484 0.144 43.222 43.479 43.768
beta3_slope[12] 43.346 0.320 42.733 43.324 44.020
beta3_slope[13] 42.503 1.477 38.980 42.989 44.328
beta3_slope[14] 44.335 0.403 43.514 44.350 44.977
beta3_slope[15] 42.100 3.253 32.740 43.494 44.296
beta3_slope[16] 43.467 0.153 43.190 43.461 43.782
beta4_slope[11] -0.436 0.228 -0.879 -0.443 0.021
beta4_slope[12] -2.338 0.780 -4.027 -2.304 -0.898
beta4_slope[13] 0.310 0.235 -0.142 0.308 0.779
beta4_slope[14] -0.032 0.281 -0.589 -0.026 0.515
beta4_slope[15] -0.136 0.219 -0.559 -0.133 0.297
beta4_slope[16] -0.058 0.249 -0.549 -0.052 0.423
sigma_H[1] 0.214 0.053 0.117 0.211 0.327
sigma_H[2] 0.173 0.029 0.124 0.172 0.236
sigma_H[3] 0.191 0.042 0.115 0.189 0.280
sigma_H[4] 0.422 0.078 0.296 0.413 0.600
sigma_H[5] 0.966 0.207 0.586 0.955 1.403
sigma_H[6] 0.401 0.193 0.061 0.391 0.818
sigma_H[7] 0.316 0.066 0.214 0.308 0.477
sigma_H[8] 0.428 0.083 0.300 0.416 0.622
sigma_H[9] 0.528 0.126 0.332 0.510 0.818
sigma_H[10] 0.210 0.040 0.142 0.207 0.300
sigma_H[11] 0.276 0.045 0.201 0.271 0.377
sigma_H[12] 0.435 0.163 0.212 0.405 0.780
sigma_H[13] 0.209 0.037 0.145 0.206 0.289
sigma_H[14] 0.513 0.095 0.346 0.506 0.721
sigma_H[15] 0.248 0.041 0.178 0.243 0.340
sigma_H[16] 0.217 0.042 0.149 0.212 0.310
lambda_H[1] 2.471 3.299 0.118 1.372 10.855
lambda_H[2] 7.505 6.808 0.653 5.549 26.861
lambda_H[3] 6.497 10.338 0.279 3.342 31.534
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 2.276 5.010 0.026 0.625 16.779
lambda_H[6] 9.033 17.568 0.008 1.298 60.695
lambda_H[7] 0.012 0.008 0.002 0.010 0.034
lambda_H[8] 8.468 10.262 0.121 5.019 35.579
lambda_H[9] 0.015 0.010 0.003 0.013 0.041
lambda_H[10] 0.282 0.612 0.031 0.182 0.957
lambda_H[11] 0.256 0.370 0.013 0.138 1.200
lambda_H[12] 4.960 6.474 0.214 2.821 22.139
lambda_H[13] 3.321 2.977 0.239 2.507 11.474
lambda_H[14] 3.644 4.398 0.236 2.196 15.477
lambda_H[15] 0.026 0.039 0.004 0.017 0.106
lambda_H[16] 0.810 1.147 0.044 0.421 4.108
mu_lambda_H[1] 4.325 1.861 1.241 4.150 8.301
mu_lambda_H[2] 3.804 1.930 0.647 3.661 7.792
mu_lambda_H[3] 3.452 1.846 0.791 3.168 7.767
sigma_lambda_H[1] 8.709 4.409 2.091 8.046 18.465
sigma_lambda_H[2] 8.388 4.693 1.092 7.813 18.397
sigma_lambda_H[3] 6.173 3.928 0.965 5.398 15.827
beta_H[1,1] 6.800 1.179 3.876 6.976 8.559
beta_H[2,1] 9.871 0.519 8.713 9.892 10.837
beta_H[3,1] 8.005 0.761 6.203 8.100 9.212
beta_H[4,1] 9.291 7.851 -6.932 9.477 24.128
beta_H[5,1] -0.160 2.505 -5.531 0.000 4.213
beta_H[6,1] 3.399 3.839 -6.510 4.762 7.627
beta_H[7,1] -0.117 6.035 -13.026 0.329 10.317
beta_H[8,1] 1.359 3.674 -2.159 1.245 3.587
beta_H[9,1] 13.286 5.686 2.297 13.230 24.511
beta_H[10,1] 7.083 1.687 3.537 7.158 10.351
beta_H[11,1] 5.341 3.280 -1.968 5.995 9.904
beta_H[12,1] 2.623 1.014 0.824 2.567 4.803
beta_H[13,1] 9.038 0.908 7.051 9.105 10.490
beta_H[14,1] 2.191 1.034 0.133 2.220 4.272
beta_H[15,1] -5.993 3.933 -13.148 -6.179 2.597
beta_H[16,1] 3.396 2.686 -0.784 3.006 9.813
beta_H[1,2] 7.889 0.258 7.350 7.895 8.367
beta_H[2,2] 10.023 0.142 9.736 10.025 10.298
beta_H[3,2] 8.958 0.192 8.574 8.958 9.330
beta_H[4,2] 3.583 1.486 0.631 3.522 6.545
beta_H[5,2] 1.916 0.970 -0.068 1.907 3.803
beta_H[6,2] 5.831 1.084 3.237 6.033 7.487
beta_H[7,2] 2.845 1.150 0.805 2.781 5.297
beta_H[8,2] 3.021 1.041 1.402 3.148 4.190
beta_H[9,2] 3.402 1.110 1.253 3.395 5.572
beta_H[10,2] 8.193 0.356 7.450 8.202 8.855
beta_H[11,2] 9.696 0.591 8.796 9.589 10.999
beta_H[12,2] 3.938 0.366 3.238 3.932 4.654
beta_H[13,2] 9.123 0.243 8.701 9.113 9.636
beta_H[14,2] 4.018 0.357 3.345 4.014 4.736
beta_H[15,2] 11.322 0.708 9.851 11.350 12.636
beta_H[16,2] 4.442 0.799 2.971 4.412 6.020
beta_H[1,3] 8.478 0.266 7.984 8.470 9.032
beta_H[2,3] 10.074 0.121 9.838 10.071 10.318
beta_H[3,3] 9.642 0.163 9.330 9.637 9.989
beta_H[4,3] -2.530 0.885 -4.316 -2.528 -0.751
beta_H[5,3] 4.005 0.658 2.713 4.021 5.270
beta_H[6,3] 8.111 1.209 6.515 7.715 10.759
beta_H[7,3] -2.972 0.701 -4.398 -2.959 -1.593
beta_H[8,3] 5.232 0.490 4.646 5.170 6.254
beta_H[9,3] -2.750 0.738 -4.212 -2.762 -1.333
beta_H[10,3] 8.725 0.282 8.157 8.728 9.276
beta_H[11,3] 8.572 0.274 7.974 8.590 9.049
beta_H[12,3] 5.246 0.326 4.475 5.290 5.746
beta_H[13,3] 8.858 0.173 8.518 8.857 9.194
beta_H[14,3] 5.682 0.273 5.094 5.698 6.181
beta_H[15,3] 10.360 0.323 9.734 10.363 10.996
beta_H[16,3] 6.145 0.584 4.883 6.190 7.141
beta_H[1,4] 8.196 0.199 7.779 8.208 8.555
beta_H[2,4] 10.114 0.127 9.838 10.123 10.336
beta_H[3,4] 10.130 0.159 9.766 10.144 10.402
beta_H[4,4] 11.770 0.455 10.838 11.772 12.630
beta_H[5,4] 5.738 0.810 4.336 5.661 7.559
beta_H[6,4] 7.213 0.909 5.035 7.502 8.411
beta_H[7,4] 8.306 0.371 7.556 8.321 9.003
beta_H[8,4] 6.678 0.248 6.201 6.691 7.079
beta_H[9,4] 7.199 0.477 6.232 7.200 8.113
beta_H[10,4] 7.723 0.235 7.279 7.712 8.199
beta_H[11,4] 9.284 0.201 8.892 9.281 9.685
beta_H[12,4] 7.120 0.213 6.724 7.118 7.536
beta_H[13,4] 9.026 0.145 8.739 9.027 9.310
beta_H[14,4] 7.675 0.214 7.269 7.674 8.101
beta_H[15,4] 9.415 0.239 8.966 9.410 9.892
beta_H[16,4] 9.268 0.235 8.846 9.250 9.779
beta_H[1,5] 8.988 0.154 8.690 8.992 9.290
beta_H[2,5] 10.782 0.095 10.604 10.777 10.984
beta_H[3,5] 10.909 0.166 10.614 10.899 11.273
beta_H[4,5] 8.413 0.470 7.529 8.400 9.381
beta_H[5,5] 5.313 0.653 3.874 5.371 6.423
beta_H[6,5] 8.797 0.607 7.985 8.648 10.369
beta_H[7,5] 6.719 0.353 6.029 6.716 7.426
beta_H[8,5] 8.205 0.220 7.845 8.194 8.641
beta_H[9,5] 8.186 0.484 7.224 8.189 9.149
beta_H[10,5] 10.116 0.223 9.671 10.123 10.547
beta_H[11,5] 11.546 0.224 11.115 11.544 11.996
beta_H[12,5] 8.474 0.203 8.069 8.468 8.871
beta_H[13,5] 10.024 0.133 9.762 10.022 10.300
beta_H[14,5] 9.206 0.236 8.775 9.194 9.686
beta_H[15,5] 11.152 0.243 10.662 11.156 11.617
beta_H[16,5] 9.924 0.174 9.563 9.927 10.251
beta_H[1,6] 10.239 0.201 9.879 10.214 10.710
beta_H[2,6] 11.527 0.109 11.306 11.529 11.743
beta_H[3,6] 10.824 0.153 10.494 10.832 11.104
beta_H[4,6] 12.844 0.827 11.126 12.876 14.394
beta_H[5,6] 5.852 0.625 4.696 5.840 7.147
beta_H[6,6] 8.789 0.659 6.898 8.909 9.720
beta_H[7,6] 9.895 0.589 8.717 9.888 11.065
beta_H[8,6] 9.520 0.280 8.978 9.543 9.964
beta_H[9,6] 8.467 0.795 6.906 8.460 10.029
beta_H[10,6] 9.511 0.315 8.839 9.535 10.067
beta_H[11,6] 10.809 0.347 10.069 10.834 11.436
beta_H[12,6] 9.366 0.254 8.877 9.360 9.898
beta_H[13,6] 11.079 0.158 10.791 11.070 11.407
beta_H[14,6] 9.895 0.300 9.304 9.892 10.472
beta_H[15,6] 10.863 0.428 10.007 10.856 11.725
beta_H[16,6] 10.521 0.246 9.949 10.540 10.962
beta_H[1,7] 10.866 0.941 8.595 11.003 12.339
beta_H[2,7] 12.231 0.441 11.302 12.245 13.108
beta_H[3,7] 10.578 0.651 9.096 10.629 11.696
beta_H[4,7] 2.544 4.248 -5.486 2.421 11.224
beta_H[5,7] 6.465 2.082 2.767 6.322 11.280
beta_H[6,7] 9.564 2.328 5.010 9.478 15.720
beta_H[7,7] 10.358 2.976 4.480 10.343 16.272
beta_H[8,7] 10.981 1.012 9.377 10.941 12.727
beta_H[9,7] 4.414 4.083 -3.669 4.457 12.405
beta_H[10,7] 9.848 1.463 7.262 9.759 12.989
beta_H[11,7] 11.004 1.686 7.846 10.871 14.658
beta_H[12,7] 9.994 0.938 7.898 10.085 11.635
beta_H[13,7] 11.674 0.733 9.998 11.760 12.871
beta_H[14,7] 10.550 0.960 8.374 10.613 12.276
beta_H[15,7] 12.088 2.227 7.619 12.109 16.438
beta_H[16,7] 12.457 1.327 10.385 12.253 15.629
beta0_H[1] 9.157 14.365 -19.449 8.978 39.516
beta0_H[2] 10.622 7.099 -4.796 10.642 24.390
beta0_H[3] 10.107 10.204 -9.220 9.932 31.209
beta0_H[4] 4.068 188.488 -376.626 9.006 372.229
beta0_H[5] 3.673 28.845 -54.719 3.990 63.496
beta0_H[6] 6.471 53.103 -110.194 7.730 111.514
beta0_H[7] 3.842 138.865 -278.641 2.807 297.456
beta0_H[8] 6.918 31.102 -15.152 6.445 28.229
beta0_H[9] 6.298 118.312 -232.498 7.572 247.650
beta0_H[10] 8.962 34.313 -60.559 9.137 76.577
beta0_H[11] 11.345 46.472 -88.038 11.213 114.014
beta0_H[12] 6.454 11.950 -16.355 6.474 27.511
beta0_H[13] 9.838 11.231 -10.210 9.593 29.097
beta0_H[14] 7.388 11.864 -14.780 7.296 29.946
beta0_H[15] 7.014 106.841 -214.761 6.981 224.695
beta0_H[16] 8.512 24.869 -43.708 8.477 62.198